Recent progress in the study of one-dimensional gravitating systems

We review recent developments in the study of two different interacting gravitational systems: the system of parallel planar mass sheets and the system of concentric spherical mass shells. The approach to equilibrium of a system of parallel planar mass sheets is investigated. Parallels with three-dimensional systems are described. Mass segregation and kinetic energy equipartition in a two-component system of planar mass sheets is demonstrated via numerical simulation. The existence of two distinct phases is demonstrated in the system of spherical mass shells. The nature of the transition in the microcanonical, canonical, and grand canonical ensembles is studied both theoretically in terms of mean-field theory and via dynamical simulation.